The smallest hyperbolic 6-manifolds.

Everitt, Brent; Ratcliffe, John; Tschantz, Steven

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Proportionality principle for cusped manifolds

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We give a short proof of the proportionality principle for cusped hyperbolic manifolds.

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The focus of this paper are questions related to how various geometric and analytical properties of hyperbolic 3-manifolds determine the commensurability class of such manifolds. The paper is for the large part a survey of recent work.

The Stable Topological-hyperbolic Space Form Problem for Complete Manifolds of Finite Volume.

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A short introduction to shadows of 4-manifolds

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We give a self-contained introduction to the theory of shadows as a tool to study smooth 3-manifolds and 4-manifolds. The goal of the present paper is twofold: on the one hand, it is intended to be a shortcut to a basic use of the theory of shadows, on the other hand it gives a sketchy overview of some of the most recent results on shadows. No original result is proved here and most of the details of the proofs are left out.